I just looked at different sizes and put them on to see which one looked best and went with that. I also used gumpaste and cut the size I wanted and let it dry and used that. but, the first time I made one, I did cover the cardboard and the cardboard ended up drooping cuz I used fondant and it didn't dry hard enough. hope this helps

You can see in my pics I have a droopy mortarboard! Made of fondant about 5 days before grad party, put it on cake the morning of, but the rain/humidity made it start to sag at the corners. Wish I had used cardboard!

After I rolled out my fondant, I put the 6" pan on top to gauge the size - I think mine ended up being a 7"x7" square - whatever looks best to you!